Method for monitoring and ensuring the safety of exothermic reactions

ABSTRACT

The invention relates to a method for monitoring exothermic reactions in a reactor, in which one or more starting materials react exothermically to give at least one product, and at least one gas is present in the reactor during operation as intended or during a runaway, comprising the following process: A) measurement and storage of an initial temperature and an initial pressure in the reactor, B) calculation of the amount of products and starting materials present in the reactor from an energy balance, C) calculation of a maximum pressure raise that occurs on stepwise reaction of the amount of starting materials present, and D) calculation of a runaway pressure from the maximum pressure raise that occurs, calculated in step C), and the measured initial pressure stored in step A).

The present invention relates to a method for monitoring andsafeguarding exothermic reactions in a reactor, in particular forsafeguarding exothermic reactions on an industrial scale. Exothermicreactions occur in numerous processes in chemistry and petrochemistry.In many cases, the liberation of energy in reaction systems of this typehas to be limited in a suitable manner for safety reasons. In the caseof deviation from operation as intended due to excessive liberation ofenergy, self-intensification of the energy release frequently occurs inreaction systems of this type, which can result in an inadmissibleincrease in pressure. The term ‘runaway’ of the reaction is used here.This increase in pressure in turn results in actuation of safety valvesand escape of product or in the admissible operating pressures of thereactor installation being exceeded.

The problem of safeguarding exothermic reactions arises to a particularextent in the case of batch reactors operated by the feed process. Here,subsidence of the reactions and simultaneous continued feed of startingmaterial can result in undesired accumulation of reactants. If thereaction re-commences in a ‘sleeping batch’ of this type, the release ofenergy owing to self-intensification is generally impossible to bringunder control. A state-of-the-art reactor for exothermic chemicalreactions therefore has complex protective devices, for example safetyvalves. Protective devices of this type are only of limited use sincetheir actuation results in escape of relatively large amounts of theproduct. This escape of product is generally unacceptable forenvironmental reasons. However, it is generally not possible, fortechnical or economic reasons, to dispose of or collect the escapedproduct in an appropriate manner since the amounts released areextremely large. Further possible safety measures are, for example, thesubject-matter of DE 297 23 396 U1, where the exothermic reaction isstopped by addition of an emergency terminator, or of DE 199 59 834 C1,where emergency cooling and pressure release of the reactor take place.

It is of considerable economic benefit for operation of a reactor ofthis type to provide a correct estimate of the potential risk of anexothermic reaction in the reactor. The safety measures mentioned aboveor others should only be taken in the case of an emergency in orderwherever possible not to lose any starting materials or products.Furthermore, the safety reserves still present should be estimated asprecisely as possible in order that the reactor can be operated underoptimum conditions.

On-line methods for the control and safeguarding of reaction systems areknown in the prior art. O. Abel, Scenario-integrated optimization ofsemi-batch reactor operation under safety constraints,Fortschritt-Berichte VDI, Series 8, No. 867, Düsseldorf, VDI-Verlag,2001, describes a method for calculating the runaway pressure as part ofa model-predictive regulator for batch reactors. The runaway pressure iscalculated as a side condition of the optimization problem in order toensure that the optimized settings of the adjustable variables(temperature, feed rate) represents safe operation even in the case offailure of the cooling. The method is restricted to semi-batchprocesses. Although this method is basically an on-line optimizationmethod, the method developed cannot be applied in real time owing to theconsiderable amount of time it requires for computation. It is thus notsuitable for monitoring an industrial reactor. Furthermore, it is not amethod for monitoring a reactor, but instead for optimizing the feedsand operating temperature. The safety aspect is only considered as aside condition in the method.

G. Deerberg, Zur sicherheitstechnischen Beurteilung vonSemi-Batch-Prozessen mit Gas-/Flüssigkeitssystemen, Environment andSafety Series Volume 1, Frauenhofer IRB-Verlag, 1997, describes a methodwhich includes calculation of the pressure in the case of a run-away. Itis attempted here to develop a simple equation for the runaway pressurewhich gives the runaway pressure with no iteration. This procedurecircumvents computation-time problems, but is generally too inaccuratefor practical applications.

WO 00/47632 relates to a method for on-line monitoring and control ofthe monomer conversion in emulsion polymerization, in which the amountof heat supplied to a reactor, the reaction enthalpy supplied throughthe monomer feed, and the amount of heat dissipated from the reactor arebalanced continuously from an initialization time, and an amount of heatwhich has not been dissipated, which, in the case of a spontaneousadiabatic reaction, would result in an increase in the internaltemperature and internal pressure of the reactor, is calculated. It ischecked whether the adiabatic temperatures and pressures thatpotentially arise are always within pre-specified upper limits. If theupper limits are exceeded, the monomer feed into the reactor is reducedor interrupted. However, the method described in WO 00/47632 is keptvery simple in the area of pressure calculation. For certainapplications (for example emulsion polymerization), the pressure modeldescribed in the patent is unsuitable in the sense that it would alsogive runaway pressure which would result in shut-down of the reactor inthe case of operation as intended.

It is an object of the present invention to provide an improved methodfor monitoring and safeguarding exothermic reactions in a reactor whichenables economic operation of the reactor at the same time as highsafety. In particular, the runaway pressure of a reaction system isestimated reliably, enabling potential states which could result in theadmissible operating pressure being exceeded to be recognized in goodtime before a risk can arise.

We have found that this object is achieved in accordance with theinvention by a method for monitoring exothermic reactions in a reactor,in which one or more starting materials react exothermically to give atleast one product, and at least one gas is present in the reactor duringoperation as intended or during a runaway, comprising the followingprocess steps:

-   A) measurement and storage of an initial temperature and an initial    pressure in the reactor,-   B) calculation of the amount of products and starting materials    present in the reactor from an energy balance,-   C) calculation of a maximum pressure raise that occurs on stepwise    reaction of the amount of starting materials present, and-   D) calculation of a runaway pressure from the maximum pressure raise    that occurs, calculated in step C), and the measured initial    pressure stored in step A).

It is accordingly proposed in accordance with the invention that themaximum pressure raise in the reactor be determined by simulation ofstepwise reaction of the starting materials present in the reactor, andthe runaway pressure be calculated by addition of this maximum pressureraise and the measured initial pressure in the reactor. Comparison ofthe calculated runaway pressure with the design limits for the reactorprovides information on the safety reserves still present. These safetyreserves can be used to optimize operation, for example to increase thefeed rate or raise the reaction temperature. The runaway pressure iscalculated continuously throughout the reaction, enabling measures forsafe termination of the reaction to be taken in good time—in particularbefore an actual runaway can be measured at all.

The method according to the invention can be applied to exothermicreactions in which at least one gas is present either during operationas intended or during a runaway. Operation as intended includesoperation for which the plant is intended, designed and suitable inaccordance with its technical purpose, and operating states which occurin the case of malfunction of components or in the case of incorrectoperation without safety reasons preventing continuation of operation oradmissible limit values being exceeded (admissible error range). The atleast one gas causes a pressure build-up in the reactor. It is presentin the reactor in the form of air, a protective gas or any desired othergas, is fed to the reactor as starting material or is formed during theexothermic reaction. The gas is formed in the exothermic reaction eitherowing to the formation of gaseous reaction products or by at leastpartial evaporation of the reactor contents or by both processes.

Simulated reaction of the amounts of starting materials present in thereactor in conversion steps enables precise determination of the maximumpressure raise occurring in the case of adiabatic runaway of the reactorthat can be achieved even before the end of the adiabatic reaction. Theend of the adiabatic reaction is reached when all the starting materialpresent has reacted and the maximum temperature has thus been reached.

In accordance with the invention, the runaway pressure that would occurduring adiabatic runaway of the reactor under the given conditions isdetermined from the calculated maximum pressure raise and the measuredinitial pressure in the reactor. Since the pressure model forcalculating initial pressure and maximum pressure raise has beenformulated conservatively in order to calculate an excessively high(i.e. safe) runaway pressure in all situations, the calculated initialpressure is higher than the measured initial pressure. Use of themeasured initial pressure in step D) of the method according to theinvention means that the error in the calculated initial pressure is notpresent in the value for the runaway pressure. The model is thereforemore accurate and enables economical operation of the reactor.

In a preferred embodiment of the present invention, the amount ofstarting materials present is divided into k part-amounts Δn forcalculating the maximum pressure raise which occurs, and the followingsteps are repeated k times:

-   a) calculation of a temperature change ΔT which arises in the    reactor and an amount of starting materials and products remaining    in the reactor on reaction of a part-amount Δn of starting materials    in the exothermic reaction,-   b) calculation of an intermediate temperature arising from the    temperature change ΔT,-   c) calculation of an intermediate pressure in the reactor using a    phase equilibrium calculation into which the intermediate    temperature, the amount of starting materials and products which    remains, and the volume of the reactor are entered as given    quantities,-   d) storage of the intermediate pressure as the starting pressure p₁    in the first run through steps a) to d),-   e) calculation of an adiabatic pressure increase as the difference    between the intermediate pressure and the starting pressure, and    -   f) storage of the adiabatic pressure increase as the maximum        pressure raise if this exceeds a value previously stored as the        maximum pressure raise.

The runaway pressure is calculated here by simulated stepwise reactionof the starting material(s) present in the reactor in k steps. Theamounts of heat fed to the reactor in any form and the amounts of heatdissipated are balanced by means of an energy balance. The amount ofstarting materials known from the energy balance (method step B)) isnotionally reacted in small amounts Δn little by little in theexothermic reaction. A temperature increase ΔT arising in the reactorafter each step arises from the amount of heat formed (reactionenthalpy), giving rise to a new intermediate temperature. For anadiabatic, closed system, the following equation, for example, applies:${{m \cdot c_{p} \cdot d}\quad T} = {\sum\limits_{i}{H_{i}d\quad n_{i}}}$where

-   m denotes the mass of the reactor contents,-   c_(p) denotes the heat capacity of the reactor contents,-   dT denotes the temperature change,-   H_(i) denotes the reaction enthalpy of the ith starting material,    and-   dn_(i) denotes the change in amount of the ith starting material.

Assuming uniform reaction of the starting materials, discretization intoequidistant reaction increments Δn_(i) gives the temperature increaseafter the jth reaction step:${\Delta\quad T_{j}} = \frac{\sum\limits_{i}{H_{i}\Delta\quad n_{i}}}{m \cdot c_{p}}$where j=1 to k (k steps)and thus the intermediate temperatureT _(j) =T _(j)−1+ΔT _(j)where

-   T_(j)−1 denotes the measured initial temperature for j=1 and the    (j−1)th intermediate temperature for j=2 to k, and-   T_(j) denotes the jth intermediate temperature after j reaction    steps.

The amounts of products and starting materials remaining in the reactorare re-calculated after each (virtual) reaction of a part-amount Δn. Forexample, the amounts of the individual substances (starting materials)are recalculated as follows after each of the k steps:n _(i,j) =n _(i,j−1) −Δn _(i)where

-   j=1 to k;-   n_(i,j) denotes the amount of the ith substance after the jth step,    and-   n_(i,0) denotes the initial amounts of substance (from the energy    balance).

An analogous relation is used to calculate the amounts of the products.

The intermediate pressure p_(j) in the system is subsequently calculatedfrom the intermediate temperature, the amounts of substance remaining,and the volume of the reactor using a phase equilibrium calculation.

The equation system for the phase equilibrium is resolved together witha constraint for the volume. This formulation of the phase equilibriumrelations is also known as VT (volume-temperature) flash. This is anon-linear equation system which can only be resolved iteratively. Informal terms, the following can be written:p _(j) =f(n _(i,j) ,T _(j) ,V)

The thermodynamic model used for the phase equilibrium makes the methodindependent of a particular recipe and results in a generally validformulation. The model is valid both for systems with and withoutseparation in the liquid phase (occurrence of two immiscible liquidphases). Special measures simplify the calculation in order to keep thecomputation time needed short (combination of components, estimation ofthe vapor pressure of water-soluble components).

In a first run through the method (first reaction step), theintermediate pressure is stored as the starting pressure p₁. In thesubsequent runs through the method, the adiabatic pressure increasearises from the difference between the current intermediate pressure andthe starting pressure. After each pressure increase calculation, it ischecked whether this is the maximum. If the current pressure increaseexceeds that in the preceding reaction steps, it is stored as themaximum pressure raise:Δp _(max)=max(p _(j))−p ₁.

Consequently, the value stored as the maximum pressure raise at the endof a pressure raise calculation corresponds to the maximum pressureincrease arising within the k reaction steps.

In a preferred embodiment of the present invention, the amount of heatfed to the reactor, the reaction enthalpy fed to the reactor throughsupplied starting materials, and the amount of heat dissipated from thereactor via reactor cooling are taken into account in the energy balancefor calculating the amount of products and starting materials present inthe reactor. The amount of heat fed to the reactor, the reactionenthalpy fed to the reactor through supplied starting materials, and theamount of heat dissipated from the reactor are determined by means oftemperature and flow-rate measurements in the reactor feeds and outflowsand in the coolant circuits. The non-dissipated heat calculated by meansof the heat balance gives, as proposed in WO 00/47632, the amount ofunreacted starting materials. The energy balance evaluated, for example,for a semi-batch reactor has, for example, the following form:$U = \frac{Q}{\sum\limits_{i}{m_{i}H_{i}}}$where

-   U denotes the instantaneous conversion,-   Q denotes the amount of energy dissipated up to the current time,-   m_(i) denotes the amount of the ith starting material metered in,-   H_(i) denotes the reaction enthalpy of the ith starting material.

With the conversion calculated in this way and assuming uniformreaction, the amounts of starting material still present in the systemm_(i,rem) is given bym _(i,rem)=(1−U)m _(i)and the substance amounts$n_{i,0} = \frac{m_{i,{r\quad e\quad m}}}{M_{i}}$

The pressure calculation is started with these remaining amounts ofstarting material and the amount of product, likewise determined fromthe calculated conversion.

In a preferred embodiment of the present invention, interactions betweenproducts and starting materials in the reactor are taken into accountwhen calculating the maximum pressure raise. For example, the vaporpressure of the substances which becomes established in the reactor isreduced in certain reaction systems due to interactions of thesubstances. A reduction in the vapor pressure of this type can be takeninto account, for example, by introducing an activity coefficient γ. Theactivity coefficient is obtained from models which describe theinteractions of the substances. The vapor pressure p_(D) in a reactorcan be calculated as part of the phase equilibrium calculation, forexample using the following formula:$p_{D} = {\sum\limits_{i}{\gamma_{i}x_{i}p_{0i}}}$where

-   γ_(i) denotes the activity coefficient of the ith component,-   x_(i) denotes the molar fraction of the ith component, and-   p_(0,i) denotes the vapor pressure of the ith component.

The present invention furthermore relates to a method for the on-linemonitoring and on-line safeguarding of exothermic reactions in areactor. In this method, a simplified model is set up using the runawaypressures calculated by the method according to the invention formonitoring exothermic reactions (as described above). This simplifiedmodel is used on-line for monitoring and safeguarding the reactor. Thereason for this is that the “rigorous” model described above is usuallytoo complicated to be implemented in the real-time environment. Use istherefore made of the simplified model, which results in a considerablyshortened computation time and significantly lower storage requirements.For certain applications, however, the rigorous model may also besuitable for real time. The simplified model is tested off-linepoint-by-point against the rigorous model in order to ensure that thesimplified model is a conservative estimate of the rigorous model. Thesimplified model likewise gives values for the intermediate pressurep _(j) =f(n _(i,j) ,T _(j) ,V)for the respective jth reaction step and consequently the associatedadiabatic pressure increase. However, it is iteration-free and gives aconservative estimate (p_(j(simple))≧p_(j(rigorous))) of theintermediate pressure in the “rigorous” model against which it has beenvalidated point-by-point. An essential advantage of this methodaccording to the invention is consequently its real-time suitability andthus its successful industrial implementation in on-line operation. Thecalculation of the maximum pressure raise and the associated runawaypressure in narrow time intervals is repeated throughout the exothermicreaction. The simplified model can comprise mathematical equations, astored data table or a combination of the two.

In a preferred embodiment of the present invention, a safety computerwhich uses the simplified model to calculate whether a runaway pressureexceeds reactor-specific limit values serves to monitor and controlexothermic reactions in a reactor. The safety computer initiates reactorsafety measures where necessary.

If the calculated runaway pressure is greater than a reactor-specificlimit value, reactor safety measures are consequently initiated. Thereactor-specific limit value here is a fixed upper limit which depends,inter alia, on the pressure resistance of the reactor. The reactorsafety measures preferably comprise one or more of the followingmeasures: reduction in the starting-material feed rate, intensificationof the reactor cooling, triggering of a terminator system anddecompression of the reactor.

The methods according to the invention can be applied to exothermicreactions which are carried out in continuous, semi-continuous or bathreaction systems. They are suitable for all types of reactor.

The present invention furthermore relates to the use of the methodsaccording to the invention for monitoring and safeguarding an emulsionpolymerization. In the emulsion polymerization, the starting materials(principally monomers, emulsifiers, water, initiators and stabilizers)are introduced in pre-specified metering amounts into a reactor in whichthe emulsified monomers are converted exothermically into polymers. Themethods according to the invention can advantageously also be used forsystems having high vapor pressures, as occur, for example, in emulsionpolymerization.

The present invention furthermore relates to the use of the methodsaccording to the invention for monitoring and safeguarding a blowdownreactor in which the product of exothermic reactions is provisionallystored. The blowdown reactor is consequently monitored and safeguardedon-line by a separate pressure calculation in accordance with the methodaccording to the invention.

The present invention is explained in greater detail below withreference to the drawing, in which:

FIG. 1 shows a diagrammatic overview of the on-line monitoring andsafeguarding of exothermic reactions,

FIG. 2 shows a flow chart for pressure calculation by the methodaccording to the invention for monitoring exothermic reactions, and

FIG. 3 shows a depiction of the calculation of the runaway pressure fromthe pressure raise and the initial pressure.

FIG. 1 shows a diagrammatic overview of the on-line monitoring andsafeguarding of exothermic reactions.

A reactor 20 usually has a stirrer 22 driven by a motor 21, and diversereactor feeds 23 and reactor outlets 24. One of the outlets 24 leads,for example, to a heat exchanger 25 and back to one of the feeds 23. Theheat exchanger in turn has a heat-exchanger feed 26 and a heat-exchangeroutlet 27. The energies 29 fed to and dissipated from the reactor aremeasured at numerous measurement points 28 in the reactor andheat-exchanger feeds 23, 26 and outlets 24, 27. An energy balance is setup, and the conversion is calculated from the energy balance 30. Theamounts of products and starting materials currently in the reactor 20are known from the conversion calculation 30. The next step iscalculation of the runaway pressure 31 for the reactor 20 by the methodaccording to the invention. On the basis of the comparison 32 of thisrunaway pressure with the maximum admissible pressure in the reactor 20,including all associated components, a decision is made on measures 33to be taken to safeguard the reactor.

FIG. 2 shows a flow chart for pressure calculation by the methodaccording to the invention for monitoring exothermic reactions. Firstly,the input quantities 1 (starting-material and product amounts from theenergy balance, measured initial temperature T₀, measured initialpressure p₀) are entered, and the pressure calculation is subsequentlyinitialized 2. At the time of initialization, all quantities to becalculated in the method according to the invention are assigned thevalue “0”, for example the maximum pressure raise (Δp_(max)=0). Theamounts of starting materials entered as input quantities are dividedinto k part-amounts Δn, and in order to carry out the subsequentpressure calculation in k conversion steps, the step counter j is set to1.

This is followed by calculation 3 of the intermediate temperature T_(j).To this end, firstly the temperature change ΔT which arises in theexothermic reaction of a part-amount Δn of the starting materials in thereactor is determined. The intermediate temperature T_(j) is given bythe total of the temperature change and the last-calculated intermediatetemperature or, in the first run through the method (j=1), the measuredinitial temperature T₀. Furthermore, the amount of starting materialsand products remaining in the reactor after conversion of a part-amountΔn is calculated.

The next step is calculation 4 of the intermediate pressure p_(j) whichwould become established as a consequence of the conversion of apart-amount Δn in the reactor. The intermediate pressure p_(j) is giveneither from a non-linear equation system in a phase equilibriumcalculation on use of the rigorous off-line model or from the relationp_(j) =f(n _(i,j) ,T _(j) ,V)on use of the simplified on-line model, which has been validatedpoint-by-point against the rigorous model.

This is followed by an enquiry 5 whether this is the first run throughthe intermediate-pressure calculation, i.e. whether the counter of thesteps j has the value “1”. If this is the case (response 6 to enquiry5=“yes”), the calculated intermediate pressure p_(j) is stored 7 as thestarting pressure p₁.

The method according to the invention is continued after the startingpressure p₁ has been stored or directly after the response 8 to theenquiry 5 is “no” through the calculation 9 of the adiabatic pressureincrease Δp_(j). This is given by the difference between the startingpressure p₁ and the intermediate pressure p_(j). This is followed by anenquiry 10 whether the adiabatic pressure increase Δp_(j) is greaterthan the maximum pressure raise Δp_(max). If this is the case (response11 to enquiry 10=“yes”), the adiabatic pressure increase Δp_(j) isstored 12 as the maximum pressure raise Δp_(max). Where appropriate, theassociated intermediate temperature T can additionally be stored inorder that the temperature T_(pmax) prevailing at the time of themaximum pressure raise Δp_(max) can be called up at the end of themethod. A negative response 13 to enquiry 10 or the storage 12 of thesaid values is followed by an enquiry 14 whether the number ofconversion steps k has been reached, i.e. whether the value of the stepcounter j corresponds to the value of k. If the response 15 is “no”, thecounter j is increased by “1” 16, and the method is repeated from thecalculation 3 of the intermediate temperature until the counter j hasreached the value k. The response 17 to the enquiry 14 is then “yes”,and the intermediate temperature T_(j=k) is stored as the endtemperature T_(end). Finally, the runaway pressure p_(d) is determined19 from the sum of the calculated maximum pressure raise ΔP_(max) andthe measured initial pressure p₀. If the runaway pressure p_(d) exceedsreactor-specific limit values, reactor safety measures are initiated inorder to prevent runaway of the reactor.

In the on-line model, the method shown in FIG. 2 by means of a flowchart is repeated at narrow time intervals until the end of thereaction, i.e. the reactor is monitored continuously.

FIG. 3 shows a depiction of the calculation of the runaway pressure fromthe pressure increase and the calculated initial pressure.

In the diagram, the reactor pressure p_(R) is plotted on the y axis, andthe amount of starting material n_(i) is plotted on the x axis. Theamount of starting material n_(i) has the value n_(i,0) at the beginningand decreases toward 0 in steps Δn_(i) along the x axis, i.e. thediagram shows reaction of the starting materials in steps of Δn_(i). Tworeactor pressure courses depending on the amount of starting materialn_(i) are shown, on the one hand the (normally unknown) actual pressurecourse in the case of a runaway 34 and on the other hand the runawaypressure 35 determined from the calculated pressure increase and thecalculated initial pressure. The measured (real) initial pressure 36here is a value of Δp₀ lower than the initial pressure 37 calculated bythe method according to the invention. The model on which the methodaccording to the invention is based furthermore gives (owing to itsconservative design) a calculated adiabatic pressure increaseΔP_(ad,mod) whose value is larger than the real pressure increaseΔP_(ad,real). Consequently, the maximum runaway pressure 38 determinedfrom the sum of the calculated initial pressure 37 and the calculatedpressure increase Δp_(ad,mod) is significantly higher than the realmaximum runaway pressure 39, which is given by the sum of the measuredreal initial pressure 36 and the real pressure increase Δp_(ad,real).Measures for safeguarding the reactor would already be implemented withconsiderable safety reserves still present in a runaway calculationcarried out in this way since the calculated maximum runaway pressure 38would, where appropriate, already exceed the maximum admissible reactorpressure. In order to achieve a more real estimation of the maximumrunaway pressure, it is therefore determined from the sum of themeasured initial pressure 36 and the calculated maximum pressure raiseΔp_(ad,mod(max)) in the method according to the invention. A maximumrunaway pressure 40 determined in accordance with the invention, whichconservatively estimates the real maximum runaway pressure 39, butnevertheless allows substantial utilization of the safety reserves inthe reactor, thus arises before measures for safeguarding the reactorare implemented.

Example of a Phase Equilibrium Calculation

The phase equilibrium calculation can be formulated in various ways. Aconventional formulation will now be presented. The following equationsare resolved here:

-   -   as balance for each component over all phases,    -   phase equilibrium condition for each component,    -   material data relations for vapor pressures, density, . . . and    -   volume constraint.

The following equations, for example, are to be resolved: 1. n_(i) =n_(i) ^(L) + n_(i) ^(V) ∀i = 1, . . . k (mass balances) 2.${x_{i} = {{\frac{n_{i}^{L}}{\sum n_{i}^{L}}\quad{\forall i}} = 1}},{\cdots\quad k}$(molar fractions) 3.${y_{i} = {{\frac{n_{i}^{V}}{\sum n_{i}^{V}}\quad{\forall i}} = 1}},{\cdots\quad k}$″ 4. y_(i) · p · φ_(i) = x_(i) · γ_(i) · p_(0,i) ∀i = 1, . . . k (phaseequilibria) 5.$V = {\frac{\sum{n_{i}^{V}\quad \cdot \quad M_{i}}}{\rho^{V}} + \frac{\sum{n_{i}^{L}\quad \cdot \quad M_{i}}}{\rho^{L}}}$(volume constraint) 6. p_(0,i) = p_(0,i) (T)  ∀i = 1, . . . k (massrelation) 7. φ_(i) = φ_(i) (T, p, y_(i)) ∀i = 1, . . . k ″ 8. γ_(i) =γ_(i) (T, x_(i))  ∀i = 1, . . . k ″ 9. ρ^(V) = ρ^(V) (y_(i), p, T) ″ 10.ρ^(L) = ρ^(L) (x_(i), T) ″where

-   n_(i) denotes the amount of component i (gas and liquid phase)-   n_(i) ^(L) denotes the amount of component i (liquid phase)-   n_(i) ^(v) denotes the amount of component i (gas phase)-   y_(i) denotes the molar fraction of component i (gas phase)-   x_(i) denotes the molar fraction of component i (liquid phase)-   p denotes the pressure-   φ_(i) denotes the fugacity coefficient of component i-   γ_(i) denotes the activity coefficient of component i-   p_(0,i) denotes the vapor pressure of pure component i-   M_(i) denotes the molecular weight of component i-   ρ_(v) denotes the density of the gas phase-   ρ^(L) denotes the density of the liquid phase-   V denotes the reactor volume-   T denotes the temperature

In total, the equation systems formed from the ten equations mentionedabove contain 9 k+5 variables. The values for the quantities n_(i),M_(i), V and T, i.e. the values for 2 k+2 quantities, are pre-specifiedin the calculation. Since the ten general equations mentioned above forman equation system with 7 k+3 individual equations, all 9 k+5 variablescan be determined.

For the mass relations (equations 6 to 10), various formulations areindicated in the prior art (for example γ via the NRTL, Flory-Huggins orUNIQUAC model, φ via the Peng-Robinson or Soave-Redlich-Kwong stateequation).

The equation system comprising the above-mentioned equations can beresolved iteratively for calculation of the intermediate pressure neededfor the calculation of the adiabatic pressure increase.

LIST OF REFERENCE NUMERALS

-   1 Entry of the input quantities-   2 Initialization-   3 Calculation of the intermediate temperature T_(j)-   4 Calculation of the intermediate pressure p_(j)-   5 Enquiry whether this is the first run (j=1?)-   6 Response to enquiry 5=“yes”-   7 Storage of the intermediate pressure p_(j) as starting pressure p₁-   8 Response to enquiry 5=“no”-   9 Calculation of the adiabatic pressure increase Δp_(j)-   10 Enquiry whether the adiabatic pressure increase is greater than    the maximum pressure raise (Δp_(j)>Δp_(max)?).-   11 Response to enquiry 10=“yes”-   12 Storage of the adiabatic pressure increase Δp_(j) as the maximum    pressure raise Δp_(max)-   13 Response to enquiry 10=“no”-   14 Enquiry whether the number of conversion steps has been reached    (j=k?)-   15 Response to enquiry 14=“no”-   16 Increase in the step counter by 1 (j=j+1)-   17 Response to enquiry 14=“yes”-   18 Storage of the intermediate temperature as the end temperature-   19 Calculation of the runaway pressure Pd-   20 Reactor-   21 Motor-   22 Stirrer-   23 Reactor feeds-   24 Reactor outlets-   25 Heat exchanger-   26 Heat-exchanger feed-   27 Heat-exchanger outlet-   28 Measurement points-   29 Measurement of the energies input and discharged-   30 Setting-up of an energy balance and conversion calculation    therefrom-   31 Calculation of the runaway pressure-   32 Runaway pressure/maximum admissible pressure comparison-   33 Measures for safeguarding the reactor-   34 Actual pressure course during a runaway-   35 Runaway pressure calculated from the calculated pressure increase    and the calculated initial pressure-   36 Measured initial pressure-   37 Calculated initial pressure-   38 Calculated maximum runaway pressure-   39 Real maximum runaway pressure-   40 Maximum runaway pressure determined in accordance with the    invention

1. A method for monitoring exothermic reactions in a reactor, in whichone or more starting materials react exothermically to give at least oneproduct, and at least one gas is present in the reactor during operationas intended or during a runaway, comprising the following process steps:A) measurement and storage of an initial temperature and an initialpressure in the reactor, B) calculation of the amount of products andstarting materials present in the reactor from an energy balance, C)calculation of a maximum pressure raise, that occurs on stepwisereaction of the amount of starting materials present, in relation to acalculated starting pressure, which is greater than the measured initialpressure and D) calculation of a runaway pressure from the maximumpressure raise that occurs, calculated in step C), and the measuredinitial pressure stored in step A).
 2. The method as claimed in claim 1,wherein, in order to calculate the maximum pressure raise that occurs(step C), the amount of starting materials present is divided into kpart amounts Δn, and the following steps are carried out k times: a)calculation of a temperature change ΔT which arises in the reactor andan amount of starting materials and products remaining in the reactor onreaction of a part-amount Δn of starting materials in the ex thermicreaction, b) calculation of an intermediate temperature ari˜ing from thetemperature change ΔT, c) calculation of an intermediate pressure in thereactor using a phase equilibrium calculation into which theintermediate temperature, the amount of starting materials and productswhich remains, and the volume of the reactor are entered as givenquantities, d) storage of the intermediate pressure as the startingpressure p₁ in the first run through steps a) to d), e) calculation ofan adiabatic pressure increase as the difference between theintermediate pressure and the starting pressure, and f) storage of theadiabatic pressure increase as the maximum pressure raise if thisexceeds a value previously stored as the maximum pressure rise.
 3. Themethod as claimed in claim 1, wherein the heat fed to the reactor, thereaction enthalpy fed to the reactor by means of supplied startingmaterials, and the amount of heat dissipated from the reactor viareactor cooling are taken into account in the energy balance (step B).4. The method as claimed in claim 1, wherein interactions betweenproducts and starting materials in the reactor are taken into accountwhen calculating the maximum pressure rise (step C).
 5. A method for theon-line monitoring and on-line safeguarding of exothermic reactions in areactor, wherein a simplified model is set up on the basis of therunaway pressures calculated by the method as claimed in claim 1, andthis simplified model is employed on-line for monitoring andsafeguarding the reactor.
 6. The method as claimed in claim 5, wherein asafety computer serves for monitoring and controlling exothermicreactions in a reactor, calculating, on the basis of the simplifiedmodel, whether the runaway pressure exceeds reator-specific limit valuesand initiating, where appropriate, reactor safety measures.
 7. Themethod as claimed in claim 6, wherein the reactor safety measurescomprises one or more of the following measures: reduction in thestarting-material feed rate, intensification of the reactocooling,triggering of a terminator system, and decompression of the reactor. 8.The method as claimed in claim 1, wherein the exothermic reactions arecarried out continuously, semi-continuously or batchwise.
 9. The use ofthe method as claimed in claim 1 wherein the exothermic reaction is anemulsion polymerization reaction.
 10. The method as claimed in claim 1wherein the reactor is a blowdown reactor in which the product of theexothermic reactions is provisionally stored.